How to make a sideways bone?
Bones in blender are not limited to one axis, thus moving them along an angle is easy.

You can constrain it to 2 axes (say X and Z by pressing SHIFT+Y after pressing G) when moving, and this is likely what you want. Insert a keyframe at the bone's resting position, then advance a few frames, and move the bone along the 2 axes so that it lines up with the grip. You can even start to rotate it after its exiting the grip. There is no need for it to follow the grip exactly, because this wont even happen in real life. Just move it approximately and you should get great results.